Econometric Theory/Methodology of Econometrics

How does the econometrician go ahead in analysing an economic theory? What is needed is a methodology, i.e. a step-by-step procedure. This is similar to other social sciences.

Theory
A theory should have a prediction. In statistics and econometrics, we also speak of hypothesis. One example is the marginal propensity to consume (MPC) proposed by Keynes. Other examples could be that lower taxes would increase growth, or maybe that it would increase economic inequality, and that introducing a common currency has a positive effect on trade.

Specification of the Mathematical Model
This is where the algebra enters. We need to use mathematical skills to produce an equation. Assume a theory predicting that more schooling increases the wage. In economic terms, we say that the return to schooling is positive. The equation is:

$$ Y = \beta_1 + \beta_2 X $$,

where Y is the variable for wage and $$ \beta_1 $$ is a constant and $$ \beta_2 $$ is the coefficient of schooling, and X is a measurement of schooling, i.e. the number of years in school. We also call $$ \beta_1 $$ intercept and $$ \beta_2 $$ a slope coefficient.

Normally, we would expect both $$ \beta_1 $$ and $$ \beta_2 $$ to be positive.

Specification of the Econometric Model
Here, we assume that the mathematical model is correct but we need to account for the fact that it may not be so. We add an error term, u to the equation above. It is also called a random (stochastic) variable. It represents other non-quantifiable or unknown factors that affect Y. It also represents mismeasurements that may have entered the data. The econometric equation is:

$$ Y = \beta_1 + \beta_2 X + u $$. The error term is assumed to follow some sort of statistical distribution. This will be important later on.

Obtaining Data
We need data for the variables above. This can be obtained from government statistics agencies and other sources. A lot of data can also be collected on the Internet in these days. But we need to learn the art of finding appropriate data from the ever-increasing loads of data.

Estimation of the model
Here, we quantify $$ \beta_1 $$ and $$ \beta_2 $$, i.e. we obtain numerical estimates. This is done by statistical technique called regression analysis.

Hypothesis Testing
Now we go back to the part where we had economic theory. The prediction was that schooling is good for the wage. Does the econometric model support this hypothesis. What we do here is called statistical inference (hypothesis testing). Technically speaking, the $$ \beta_2 $$ coefficient should be greater than 0

if schooling is positively effect on wages (accept the hypothesis).

Forecasting or Prediction
If the hypothesis testing was positive, i.e. the theory was concluded to be correct, we forecast the values of the wage by predicting the values of education. For example, how much would someone earn for an additional year of schooling? If the X variable is the years of schooling, the $$ \beta_2 $$ coefficient gives the answer to the question.

Use for Policy Recommendation
Lastly, if the theory seems to make sense and the econometric model was not refuted on the basis of the hypothesis test, we can go on to use the theory for policy recommendation. If your theory was really good, then maybe you will earn the Nobel Prize of Economics.